defects and impurities in oxide semiconductors

Defects and doping in oxides: What we have learned so farAnderson JanottiMaterials Department, University of California Santa Barbara

Tuesday, February 23, 2010

Collaborators

J. Varley, J. Lyons, J. Weber, C. G. Van de Walle (Materials Dept., UCSB)P. Rinke, M. Scheffler (MPI-Berlin, UCSB)S. Limpijumnong, P. Reunchan (Suranaree Univ. of Tech. Thailand)G. Kresse, University of ViennaT. Ive, O. Bierwagen, J. Speck (Materials Dept., UCSB)M. McCluskey (Washington State University)G. D. Watkins (Lehigh University) L. Halliburton (West Virginia University)S. Chambers (Pacific Northwestern Nat. Lab)


Variety of crystal structures and band gaps

Material Crystal structutre Band gap (eV)ZnO wurtzite 3.4TiO2 Anatase, rutile 3.0 - 3.4SnO2 rutile 3.6In2O3 bixbyte 2.7

ZnO-based “Invisible” electronics

Available as large single crystals

2-inch ZnO wafer grown by Eagle-Picher Technologies

Diebold, Surf. Sci. Rep. (2003)

Transparent transistors, Wager, Science (2003)

Murai et al, phys. stat. sol. (2007)

ZnO transparent electrode: Mega cone

Possible applications• light emitting diodes and laser diodes• transparent electronics• electronic “noses” (gas sensors)• photocatalysis, water splitting• transparent electrodes, smart widows

Oxide semiconductors

ZnO TiO2


Major problem: controlling the conductivityVision


Controlling the conductivity is a major problem

• High levels of unintentional n-type conductivity– traditionally attributed to native point defects: oxygen

vacancies and/or cation interstitials

– conductivity varies inversely with oxygen partial pressure

• Difficult to make p-type– valence band is low in energy in an absolute scale

– stability and reproducibility are main issues (p-ZnO)

Kroger, The Chemistry of imperfect crystals, (North-Holland Publishing Co., Amsterdam, 1964)Tomlins, Routbort, and Mason, J. Appl. Phys. Rev. 87, 117 (2000)Look, et al., Phys. Rev. Lett. 82, 2552 (1999), Phys. Rev. Lett. 95, 225502 (2005)Hartnagel and Dawar, Semiconducting Transparent Thin Films, (IOP, Bristol, 1995)

Goal: understand the effects of native defects and impurities by performing first-principles calculations (DFT-LDA and beyond)


Ef(V q

O) = Et(V

qO)− Et(ZnO) +

1

2Et(O2) + µO + q�F

µZn + µO = ∆Hf (ZnO)

c = N0e−βEf

�VBM ≤ �F ≤ �CBM

First-principles formalism

Ex.: Oxygen vacancy in ZnO

Determine concentra7ons/solubility

O-‐rich, Zn-‐rich condi7ons

p-‐type, n-‐type

Transition levels (shallow/deep donor/acceptor) Migration barriers (stability) Optical transitions - configuration coordinate diagrams Frequencies of local vibration modes

Formation energies

VASP: periodic boundary condi7ons, plane-‐wave basis set, special k points, projector augmented poten7als (PAW)


Oxygen vacancy in ZnO cannot be described by DFT-LDA

Electrically active - introduces levels in the gap Possible charge states: 0, +1, +2, Optically active - sub band-gap transitions Cannot be described in DFT-LDA/GGA ?

LDA/GGA

VBM

CBM

0.8 eV

Zn dbs

The band gap is drastically underestimated in DFT-LDA/GGA0.8 eV (LDA/GGA) vs. 3.4 eV (Expt.)


Approaches to overcome the band gap problemLDA+U

U applied to semicore d states ➙ partial correction of band gaps extrapolation from LDA and LDA+U calculations ex: ZnO, InN, GaN, SnO2, In2O3

Screened hybrid functional (Heyd, Scuseria, Einzernhof)

mix of Hartree-Fock and GGA/LDA exchange ➙ removes self-interaction band gaps in agreement with experiments (by tuning mixing parameter)

more general, can be applied to any semiconductor/material ex: ZnO, InN, TiO2, SrTiO3

GW correct band gaps

combined with LDA ➙ correct formation energies and transition levels ex: Si, MgO


Combining LDA and LDA+U to overcome theband gap problemLDA+U


p-d repulsion

gap

d states

VBM (O p states)

CBM (Zn s states)

LDA+U: d bands are lowered with respect to VBMThe band gap is partially corrected: LDA: 0.8; LDA+U 1.5; Exp. 3.4 eV


Combining LDA and LDA+U to overcome theband gap problemLDA+U


p-d repulsion

gap

d states

VBM (O p states)

CBM (Zn s states)

LDA+U: affects both valence band and conduction band


Correcting transition levels and formation energies based on LDA/LDA+U calculations

Appl. Phys. Lett. 87, 122102 (2005)

!(q/q!) =!(q/q!)LDA+U

! !(q/q!)LDA

ELDA+Ug ! ELDA

g

(Eexpg ! ELDA+U

g ) + !(q/q!)LDA+U

Take into account valence vs. conduction band character of the defect state in the gap


Deep donor (2+/0) at 1 eV below CBMcannot cause conductivity

+1 charge state unstable EPR active, need light excitation to see +1

High formation energy in n-typeLow concentrations in equilibrium conditionsIn agreement with Watkins & Vlasenko Phys. Rev. B 71, 125210 (2005): +1 only observed after irradiation

Zn-rich

Form

atio

n en

ergy

(eV

)Oxygen vacancy in ZnO


Oxygen vacancy in ZnOElectronic proper7es strongly coupled with local laLce relaxa7ons


VO in ZnO: comparison with experiment

Ea! Ee!

�F @CBM

Vlasenko & Watkins, Phys. Rev. B 71, 125210 (2005).


• VO, VZn: dominant defects– Janotti and Van de Walle,Phys. Rev. B 76, 165202 (2007)– Zhang et al., Phys. Rev. B 63, 075205 (2001)– Oba et al., Phys. Rev. B 77, 245202 (2008).

• VO: deep donor– Also high formation energy inn-type ZnO

• VZn: deep acceptor– Cause of green luminescence– Kohan, et al. Phys. Rev. B 61, 15019 (2000)– Janotti and Van de Walle, Phys. Rev. B 76, 165202 (2007)

• Zni: high formatio energyunstable, migration barrier 0.57 eV

Native point defects in ZnO


Native defects vs. impurities

• Native defects cannot explain n-type doping• Impurities: donors?


Interstitial hydrogen in ZnO


Substitutional hydrogen in ZnO


Diffusion of substitutional hydrogen

How does HO move?

Dissociation:HO+ → Hi+ + VO0 costs 3.8 eV!


Diffusion of substitutional hydrogen

2.5 eV

How does HO move?

Dissociation:HO+ → Hi+ + VO0 costs 3.8 eV!

Migration:– Concerted exchange of H and neighboring O– Barrier: 2.5 eV⇒ becomes mobile above 500 ºC

• Consistent with experimentalobservations– Shi et al., Phys. Rev. B 72,195211 (2005)– Jokela and McCluskey, Phys. Rev. B 72, 113201 (2005)


Hydrogen multicenter bonds


Nitrogen doping in ZnO

In principle, the most promising p-type dopant in ZnO

Experimental results are highly controversial

Stability and reproducibility are main issues


ZnO: Hybrid functional calculations

ZnO band structure


NO in ZnO

Lyons, Janotti, and Van de Walle, Appl. Phys. Lett. 95, 252105 (2009)

Deep acceptor

Will not lead to p-type conductivity


NO in ZnO – theory vs. experiment

Lyons, JanoL, and Van de Walle, Appl. Phys. LeO. 95, 252105 (2009)

Annealed in air

Garces et al., Appl. Phys. LeO. 80, 1334 (2002)


NO in ZnO: theory vs. experiment

Lyons, JanoL, and Van de Walle, Appl. Phys. LeO. 95, 252105 (2009)

Anisotropy in the spin density


Oxygen vacancy in TiO2

LDA/GGA functionals can describe only +2 charge state Electrons from 0 and +1 charge states go to the conduction band

LDA/GGALDA/GGA

?

LDA/GGA

Is DFT-LDA/GGA enough?


Ru7le

TiO2:Hybrid functional calculations


TiO2: GGA vs. Hybrid functional (HSE)

Phys. Rev. B 81, 085212 (2010)Tuesday, February 23, 2010

relaxed VO0 and VO+ can be described in HSE

VO in TiO2: GGA vs. HSE


gap states have strong contributions from the two out-of-plane Ti atoms

VO0 and VO+ charge distributions

spin=0 spin=1/2, paramagne7c


shallow donor - can cause conductivity low formation energy only in extreme O-poor conditions

VO in TiO2: HSE results


Summary

LDA/LDA+U scheme • Limited to systems with semicore d states• Computationally inexpensive, large systems (>200 atoms)

Hybrid functionals (HSE)• Mixing parameter and screening length• Can be applied to any semiconductor • Computationally demanding (~100 atoms, few k-points)


SummaryZnO

Native defects are not the cause of unintentional n-type conductivity

Impurities are the likely cause (hydrogen) Nitrogen doping not lead to p-type ZnO

TiO2

Oxygen vacancy is a shallow donor Low formation energy only in extreme O-poor Need to relate µO to realistic conditions


Janotti & Van de Walle PRB 76, 165202 (2007)

Oba et al., PRB 77, 245202 (2008)

LDA/LDA+U vs. HSE


Diffusion of point defects


Annealing temperature of point defects


Si and Ge in ZnO

Phys. Rev. B 80, 205113 (2009)• Si and Ge are shallow donors• [Si] of up to 10E17 cm-3 observed in as grown single crystals McCluskey and Jokela, Physica B 401-402, 355 (2007)


defects and impurities in oxide semiconductors

Documents